Optimism Bias - A Better than Average Rant

I have been exercised to write because of a misapprehension, or at least sloppy terminology, seen in a recent psychology talk at a university, and on Australia's national science TV show Catalyst (this story). The phenomenon being mentioned in both cases is something known as the optimism bias, among other names. You can read about it on this wikipedia page.

The basic idea is that for some quality X, an excessive number (a majority or a very big majority, called a supermajority) of people assume they have above the norm values of X. Now to be properly a fallacy, in the sense of being a logical impossibility rather than a simple factual error, we really need to find that a majority of people assume they have above-median levels of X. More than a majority claiming above-median levels of X mean that someone is wrong.

The usual presentation of the fallacy, and this is the form in the Catalyst story, is that for some quality X a majority of people believe they have above-average levels of X. This statement doesn't work as a logical fallacy. The wikipedia page (in the section on skewed distributions) points out that most people have an above-average number of legs (since we have a large majority of 2-legged people, and people with fewer than 2 legs). Similarly, most people: have above-average numbers of kidneys; have committed fewer-than-average crimes; have practiced less-than-average cannibalism; have names more-than-averagely non-identical with Donald Duck (at least one non-cartoon Scot holds this name); and most people in Australia hold more than the average number of drivers licenses.

Let's look at the drivers license in detail. Many people in the Australia do not hold a drivers license (eg minors), many people hold one drivers license, very few hold two or more. The average number of drivers licenses per person in this country is between 0 and 1. Since more people have a drivers license than not, the majority of Australians hold more-than-average numbers of drivers licenses.

Now, it is entirely possible that people are more optimistic about their abilities as drivers or share traders than they should be. On a reasonable scale of abilities, maybe too many believe they are above average. But this is not a logical fallacy as presented, merely an error of fact, where the fact in error is the skew in the distribution.